Intuitionistic proof transformations and their application to constructive program synthesis

Abstract

We present a translation of intuitionistic sequent proofs from a multi-succedent calculus LTmc into a single-succedent calculus LT. The former gives a basis for automated proof search whereas the latter is better suited for proof presentation and program construction from proofs in a system for constructive program synthesis. Well-known translations from the literature have a severe drawback; they use cuts in order to establish the transformation with the undesired consequence that the resulting program term is not intuitive. We establish a transformation based on permutation of inferences and discuss the relevant properties with respect to proof complexity and program terms.

The research report is supported by the German Academic Exchange Service DAAD with a fellowship to the second author.